DATR Theories and DATR Models 
Bill Keller 
School of Cognitive and Computing Sciences 
The University of Sussex 
Brighton, UK 
email: billk@cogs.susx.ac.uk 
Abstract 
Evans and Gazdar (Evans and Gazdar, 
1989a; Evans and Gazdar, 1989b) intro- 
duced DATR as a simple, non-monotonic 
language for representing natural language 
lexicons. Although a number of implemen- 
tations of DATR exist, the full language has 
until now lacked an explicit, declarative se- 
mantics. This paper rectifies the situation 
by providing a mathematical semantics for 
DATR. We present a view of DATR as a lan- 
guage for defining certain kinds of partial 
functions by cases. The formal model pro- 
vides a transparent treatment of DATR's 
notion of global context. It is shown that 
DA-I'R's default mechanism can be accoun- 
ted for by interpreting value descriptors as 
families of values indexed by paths. 
1 Introduction 
DATR was introduced by Evans and Gazdar (1989a; 
1989b) as a simple, declarative language for repre- 
senting lexical knowledge in terms of path/value 
equations. The language lacks many of the con- 
structs found in general purpose, knowledge repre- 
sentation formalisms, yet it has sufficient expressive 
power to capture concisely the structure of lexical 
information at a variety of levels of linguistic des- 
cription. At the present time, DATR is probably the 
most widely-used formalism for representing natu- 
ral language lexicons in the natural language pro- 
cessing (NLP) community. There are around a do- 
zen different implementations of the language and 
large DATR lexicons have been constructed for use 
in a variety of applications (Cahill and Evans, 1990; 
Andry et al., 1992; Cahill, 1994). DATR has been 
applied to problems in inflectional and derivational 
morphology (Gazdar, 1992; Kilbury, 1992; Corbett 
and Fraser, 1993), lexical semantics (Kilgariff, 1993), 
morphonology (Cahill, 1993), prosody (Gibbon and 
Bleiching, 1991) and speech (Andry et al., 1992). In 
more recent work, the language has been used to 
provide a concise encoding of Lexicalised Tree Ad- 
joining Grammar (Evans et al., 1994; Evans et al., 
1995). 
A primary objective in the development of DATR 
has been the provision of an explicit, mathematically 
rigorous semantics. This goal was addressed in one 
of the first publications on the language (Evans and 
Gazdar, 1989b). The definitions given there deal 
with a subset of DATR that includes core features of 
the language such as the notions of local and global 
inheritance and DATR's default mechanism. Howe- 
ver, they exclude some important and widely-used 
constructs, most notably string (or 'list') values and 
evaluable paths. Moreover, it is by no means clear 
that the approach can be generalized appropriately 
to cover these features. In particular, the formal ap- 
paratus introduced by Evans and Gazdar in (1989b) 
provides no explicit model of DATR's notion of glo- 
bal contexL Rather, local and global inheritance are 
represented by distinct semantic functions £: and G. 
This approach is possible only on the (overly restric- 
tive) assumption that DArR statements involve eit- 
her local or global inheritance relations, but never 
both. 
The purpose of the present paper is to remedy 
the deficiencies of the work described in (Evans and 
Gazdar, 1989b) by furnishing DATR with a trans- 
parent, mathematical semantics. There is a stan- 
dard view of DATR as a language for representing a 
certain class of non-monotonic inheritance networks 
('semantic nets'). While this perspective provides 
an intuitive and appealing way of thinking about the 
structure and representation of lexical knowledge, it 
is less clear that it provides an accurate or particu- 
larly helpful picture of the DATR language itself. In 
fact, there are a number of constructs available in 
DATR that are impossible to visualize in terms of 
simple inheritance hierarchies. For this reason, the 
work described in this paper reflects a rather diffe- 
rent perspective on DATR, as a language for defining 
certain kinds of partial functions by cases. In the fol- 
lowing sections this viewpoint is made more precise. 
Section 2 presents the syntax of the DATR language 
and introduces the notion of a DATR theory. An 
55 
informal introduction to the DATR language is pro- 
vided, by example, in section 3. The semantics of 
DATR is then covered in two stages. Section 4.1 
introduces DATR interepretations and describes the 
semantics of a restricted version of the language wit- 
hout defaults. The treatment of implicit information 
is covered in section 4.2, which provides a definition 
of a default model for a DATR theory. 
2 DATR Theories 
Let NODE and ATOM be disjoint sets of symbols (the 
nodes and atoms respectively). Nodes are denoted 
by N and atoms by a. The set DESC of DATR value 
descriptors (or simply descriptors) is built up from 
the atoms and nodes as shown below. Descriptors 
are denoted by d. 
• a E DESC for any a E ATOM 
• For any N E NODE and dl...dn E DESC: 
N : (dl'"dn) E DESC 
"N : (dl --.dn)" E DESC 
"(dl "-'dn)" • DESC 
"N" • DESC 
Value descriptors are either atoms or inheritance 
descriptors, where an inheritance descriptor is fur- 
ther distinguished as either local (unquoted) or glo- 
bal (quoted). There is just one kind of local descrip- 
tor (node/path), but three kinds of global descriptor 
(node/path, path and node) 1 
A path (al...an) is a (possibly empty) sequence 
of atoms enclosed in angle brackets. Paths are deno- 
ted by P. For N a node, P a path and a • ATOM* a 
(possibly empty) sequence of atoms, an equation of 
the form N : P = a is called an extensional sentence. 
Intuitively, an extensional sentence N : P = a states 
that the value associated with the path P at node 
N is a. For ¢ a (possibly empty) sequence of value 
descriptors, an equation of the form N : P == ¢ 
is called a definitional sentence. A definitional sent- 
ence N : P --- ¢ specifies a property of the node N, 
namely that the path P is associated with the value 
defined by the sequence of value descriptors ¢. 
A collection of equations can be used to specify the 
properties of different nodes in terms of one another, 
and a finite set of DATR sentences 7- is called a DATR 
theory. In principle, a DATR theory 7" may consist 
of any combination of DATR sentences, either defini- 
tional or extensional, but in practice, DATR theories 
are more restricted than this. The theory 7- is said 
to be definitional if it consists solely of definitional 
sentences and it is said to be functional if it meets 
the following condition: 
1The syntax presented in (Evans and Gazdar, 1989a; 
Evans and Gazdar, 1989b) permits nodes and paths to 
stand as local descriptors. However, these additional 
forms can be viewed as conventional abbreviations, in 
the appropriate syntactic context, for node/path pairs 
N : P == ~b and N : P == ¢ E 7" implies ~b = ¢ 
There is a pragmatic distinction between defini- 
tional and extensional sentences akin to that drawn 
between the language used to define a database and 
that used to query it. DATR interpreters conventio- 
nally treat all extensional sentences as 'goal' state- 
ments, and evaluate them as soon as they are en- 
countered. Thus, it is not possible, in practice, to 
combine definitional and extensional sentences wi- 
thin a theory 2. Functionality for DATR theories, as 
defined above, is really a syntactic notion. Howe- 
ver, it approximates a deeper, semantic requirement 
that the nodes should correspond to (partial) func- 
tions from paths to values. 
In the remainder of this paper we will use the term 
(DATR) theory always in the sense functional, defi- 
nitional (DATR) theory. For a given DATR theory 
7" and node N of 7", we write 7"/N to denote that 
subset of the sentences in 7" that relate to the node 
N. That is: 
T/N = {s e 7-Is = N : P == ~b} 
The set TIN is referred to as the definition of N (in 7-). 
3 An Overview of DATR 
An example of (a fragment of) a DATR theory is 
shown in figure 1. The theory makes use of some 
standard abbreviatory devices that enable nodes 
and/or paths to be omitted in certain cases. For 
example, sets of sentences relating to the same node 
are written with the node name implicit in all but 
the first-given sentence in the set. Also, we write 
See : 0 == Verb to abbreviate the definitional 
sentence See: 0 == Verb : 0, and similarly else- 
where. 
The theory defines the properties of seven nodes: 
an abstract Verb node, nodes EnVerb, Aux and 
Modal, and three abstract lexemes Walk, Mow 
and Can. Each node is associated with a collec- 
tion of definitional sentences that specify values as- 
sociated with different paths. This specification is 
achieved either explicitly, or implicitly. Values given 
explicitly are specified either directly, by exhibiting 
a particular value, or indirectly, in terms of local 
and/or global inheritance. Implicit specification is 
achieved via DATR's default mechanism. 
For example, the definition of the Verb node gives 
the values of the paths (syn cat) and (syn type) 
directly, as verb and main, respectively. Similarly, 
the definition of Walk gives the value of (mor root / 
directly as walk. On the other hand, the value of 
2It is not clear why one would wish to do this anyway, 
but the possibility is explicitly left open in the original 
definitions of (Evans and Gazdar, 1989a). 
56 
Verb : 
EnVerb : 
Aux : 
Modal : 
Walk : 
Mow : 
Can : 
(syn cat) == verb 
(syn type) == main 
(mor form)== "(mor "(syn form)")" 
(mor pres) == "(mor root)" 
(mor past) == "(mor root)" ed 
(mor pres part) --= "(mor root)" ing 
(mor pres sing three) == "(mor root)" 
0 == Verb 
(mor past part) == "(mor root)" en 
0 == Verb 
(syn type) == aux 
0 == Aux 
(mor pres sing three) == "(mor root)" 
0 == Verb 
(mor root) == walk 
0 == EnVerb 
(mor root) --= mow 
0 == Modal 
(mor root) == can 
(mor past) == could 
Figure 1: A DATR Theory 
the empty path at Walk is given indirectly, by local 
inheritance, as the value of the empty path at Verb. 
Note that in itself, this might not appear to be par- 
ticularly useful, since the theory does not provide an 
explicit value for the empty path in the definition of 
Verb. However, DATR's default mechanism permits 
any definitional sentence to be applicable not only 
to the path specified in its left-hand-side, but also 
for any rightward extension of that path for which 
no more specific definitional sentences exist. This 
means that the statement Walk : 0 == Verb : 0 
actually corresponds to a class of implicit definitio- 
nal sentences, each obtained by extending paths on 
the left- and the right-hand-sides of the equation in 
the same manner. Examples include the following: 
Walk: (mor) == Verb: (mor) 
Walk: (mor form) =- Verb: (mor form) 
Walk : (syn cat) == Verb : (syn cat) 
Thus, the value associated with (syn cat) at 
Walk is given (implicitly) as the value of (syn cat) 
at Verb, which is given (explicitly) as verb. Also, 
the values of (mor) and (mor form), amongst 
many others, are inherited from Verb. In the same 
way, the value of (syn cat) at Mow is inherited lo- 
cally from EnVerb (which in turn inherits locally 
from Verb) and the value of (syn cat) at Can is 
inherited locally from Modal (which ultimately gets 
its value from Verb via Aux). Note however, that 
the following sentences do not follow by default from 
the specifications given at the relevant nodes: 
Walk: (mor root) == Verb: (mor root) 
Can: (mor past) == Modal: (mor past) 
Aux: (syn type) == Verb: (syn type) 
In each of the above cases, the theory provides an 
explicit statement about the value associated with 
the indicated path at the given node. As a result 
the default mechanism is effectively over-ridden. 
In order to understand the use of global (i.e. quo- 
ted) inheritance descriptors it is necessary to intro- 
duce DATR's notion of a global context. Suppose 
then that we wish to determine the value associated 
with the path (mor pres) at the node Walk. In 
this case, the global context will initially consist of 
the node/path pair Walk//mor pres). Now, by de- 
fault the value associated with (mor pres) at Walk 
is inherited locally from (mor pres) at Verb. This, 
in turn, inherits globally from the path (mor root). 
That is: 
Verb: (mor pres) == "(mor root)" 
Consequently, the required value is that associated 
with (mor root) at the 'global node' Walk (i.e. 
the node provided by the current global context), 
which is just walk. In a similar fashion, the value 
57 
Verb I 
 nV°*Ul I I L TM 
Mow I Modal\[ 
I Can I 
Figure 2: A Lexical Inheritance Hierarchy 
associated with (mor past) at Walk is obtained as 
walk ed (i.e. the string of atoms formed by evalua- 
ting the specification "(mor root)" ed in the global 
context Walk/(mor past)). 
More generally, the global context is used to fill in 
the missing node (path) when a global path (node) 
is encountered. In addition however, the evalua- 
tion of a global descriptor results in the global con- 
text being set to the new node/path pair. Thus in 
the preceding example, after the quoted descriptor 
"(mor root)" is encountered, the global context ef- 
fectively becomes Walk / (mor root) (i.e. the path 
component of the global context is altered). Note 
that there is a real distinction between a local inhe- 
ritance descriptor of the form N : P and it's global 
counterpart "N : P'. The former has no effect on 
the global context, while the latter effectively over- 
writes it. 
Finally, the definition of Verb in the theory of 
figure 1 illustrates a use of the 'evaluable path' con- 
struct: 
Verb: (mor form) == "(mor "(syn form)")" 
This states that the value of (mot form) at Verb 
is inherited globally from the path (mor...), where 
the dots represent the result of evaluating the global 
path "(syn form)" (i.e. the value associated with 
(syn form) in the prevailing global context). Eva- 
luable paths provide a powerful means of capturing 
generalizations about the structure of lexical infor- 
mation. 
4 DATR Models 
To a first level of approximation, the DATR theory 
of figure 1 can be understood as a representation of 
an inheritance hierarchy (a 'semantic network') as 
shown in figure 2. In the diagram, nodes are written 
as labelled boxes, and arcs correspond to (local) in- 
heritance, or isa links. Thus, the node Can inherits 
from Modal which inherits from Aux which in turn 
is a Verb. The hierarchy provides a useful means of 
visualising the overall structure of the lexical know- 
ledge encoded by the DATR theory. However, the 
semantic network metaphor is of far less value as 
a way of thinking about the DATR language itself. 
Note that there is nothing inherent in DATR to en- 
sure that theories correspond to simple isa hierar- 
chies of the kind shown in the figure. What is more, 
the DATR language includes constructs that cannot 
be visualized in terms of simple networks of nodes 
connected by (local) inheritance links. Global inhe- 
ritance, for example, has a dynamic aspect which is 
difficult to represent in terms of static links. Simi- 
lar problems are presented by both string values and 
evaluable paths. Our conclusion is that the network 
metaphor is of primary value to the DATR user. In 
order to provide a satisfactory, formal model of how 
the language 'works' it is necessary to adopt a diffe- 
rent perspective. 
DATR theories can be viewed semantically as coll- 
ections of definitions of partial functions ('nodes' in 
DATR parlance) that map paths onto values. A mo- 
del of a DATR theory is then an assignment of func- 
58 
tions to node symbols that is consistent with the 
definitions of those nodes within the theory. This 
picture of DATR as a formalism for defining partial 
functions is complicated by two features of the lan- 
guage however. First, the meaning of a given node 
depends, in general, on the global context of inter- 
pretation, so that nodes do not correspond directly 
to mappings from paths to values, but rather to func- 
tions from contexts to such mappings. Second, it is 
necessary to provide an account of DATR's default 
mechanism. It will be convenient to present our ac- 
count of the semantics of DATR in two stages. 
4.1 DATR Interpretations 
This section considers a restricted version of DATR 
without the default mechanism. Section 4.2 then 
shows how implicit information can be modelled by 
treating value descriptors as families of values in- 
dexed by paths. 
Definition 4.1 A DATR interpretation is a triple 
I = (U, I¢, F), where 
1. U is a set; 
2. ~ is a function assigning to each element of the 
set (U x V*) a partial funclion from (U x U*) 
to U*. 
3. F is a valuation function assigning to each node 
N and atom a an element of U, such that di- 
stinct atoms are assigned distinct elements. 
Elements of the set U are denoted by u and ele- 
ments of U* are denoted by v. Intuitively, U* is the 
domain of (semantic) values/paths. Elements of the 
set C = (U x U*) are called contexts and denoted 
by c. The function t¢ can be thought of as mapping 
global contexts onto (partial) functions from local 
contexts to values. The function F is extended to 
paths, so that for P = (ax.-.a,~) (n > 0) we write 
F(P) to denote Ul ...un E U*, where ui = F(ai) for 
each i (1 < i < n). 
Intuitively, value descriptors denote elements of 
U* (as we shall see, this will need to be revised later 
in order to account for DATR's default mechanism). 
We associate with the interpretation I = (U, t:, F) a 
partial denotation function D : DESC -'-+ (C -+ U*) 
and write \[d\], to denote the meaning (value) of de- 
scriptor d in the global context c. The denotation 
function is defined as shown in figure 3. Note that 
an atom always denotes the same element of U, re- 
gardless of the context. By contrast, the denotation 
of an inheritance descriptor is, in general, sensitive 
to the global context c in which it appears. Note 
also that in the case of a global inheritance descrip- 
tor, the global context is effectively altered to reflect 
the new local context c'. The denotation function is 
extended to sequences of value descriptors in the ob- 
vious way. Thus, for ¢ =dl .. "dn (n >_ 0), we write 
\[¢\],todenotevl.-.vn E U* ifvi = \[di\]c (1 < i < n) 
is defined (and \[¢\], is undefined otherwise). 
Now, let I = (U, s, F) be an interpretation and 
7" a theory. We will write \[T/N\]c to denote that 
partial function from U* to U* given by 
\[T/N\], = U {(F(P), \[¢\],)} 
N:P==~bE~T 
It is easy to verify that \[T/N\], does indeed denote a 
partial function (it follows from the functionality of 
the theory 7-). Let us also write \[N\], to denote that 
partial function from U* to U* given by \[N\],(v) = 
~(c)(F(N),v), for all v e U*. Then, I models 7- 
just in case the following containment holds for each 
node N and context c: 
\[N\], _.D \[T/N\], 
That is, an interpretation is a model of a DATR 
theory just in case (for each global context) the func- 
tion it associates with each node respects the defini- 
tion of that node within the theory. 
4.2 Implicit Information and Default 
Models 
The notion of a model presented in the preceding 
section is too liberal in that it takes no account of 
information implicit in a theory. For example, con- 
sider again the definition of the node Walk from the 
theory of figure 1, and repeated below. 
Walk: 0==Verb 
(mor root) == walk 
According to the definition of a model given previ- 
ously, any model of the theory of figure 1 will as- 
sociate with the node Walk a function from paths 
to values which respects the above definition. This 
means that for every global context c, the following 
containment must hold3: 
\[Walk\], ~ {(0, \[Verb: 0\]*), 
((mor root), walk)} 
On the other hand, there is no guarantee that a 
given model will also respect the following contain- 
ment: 
\[Walk\]e _D {((mor), \[Verb: (mor)\],), 
((mor root root),walk)} 
In fact, this containment (amongst other things) 
should hold. It follows 'by default' from the state- 
ments made about Walk that the path (mor) inhe- 
rits locally from Verb and that the value associated 
with any extension of (mor root) is walk. 
3In this and subsequent examples, syntactic ob- 
jects (e.g.walk, (mor root)) are used to stand for 
their semantic counterparts under F (i.e. F(walk), 
F((mor root)), respectively). 
59 
\[a\]c 
~'N: (dl--.d.)lo 
\["N: (dl """ d,)"\]~ 
\["(dx'.. d.)'l. 
\["N"\]¢ 
= F(a) 
if vi = ~di\]c is defined for each i (1 < i < n), then 
= t~(c)(F(N),vl.. "vn) 
undefined otherwise 
if vi = \[di\]e is defined for each i (1 < i < n), then 
i¢(c')(d) where d = (F(N), vl ... vn) 
undefined otherwise 
if vi = \[di\]e is defined for each i (1 < i < n), then 
= ~¢(d)(d) where c = (u, v) and d = (u, Vl..-v,) 
undefined otherwise 
= i¢(d)(e) where c = (u, v) and d= (F(N), v) 
Figure 3: Denotation function for DATR Descriptors 
There have been a number of formal treatments of 
defaults in the setting of attribute-value formalisms 
(Carpenter, 1993; Bouma, 1992; Russell et al., 1992; 
Young and Rounds, 1993). Each of these approa- 
ches formalizes a notion of default inheritance by 
defining appropriate operations (e.g. default unifi- 
cation) for combining strict and default information. 
Strict information is allowed to over-ride default in- 
formation where the combination would otherwise 
lead to inconsistency (i.e. unification failure). In 
the case of DATR however, the formalism does not 
draw an explicit distinction between strict and de- 
fault values for paths. In fact, all of the information 
given explicitly in a DATR theory is strict. The non- 
monotonic nature of DATR theories arises from a 
general, default mechanism which 'fills in the gaps' 
by supplying values for paths not explicitly speci- 
fied in a theory. More specifically, DATR's default 
mechanism ensures that any path that is not expli- 
citly specified for a given node will take its definition 
from the longest prefix of that path that is specified. 
Thus, the default mechanism defines a class of im- 
plicit, definitional sentences with paths on the left 
that extend paths found on the left of explicit sent- 
ences. Furthermore, this extension of paths is also 
carried over to paths occurring on the right. In ef- 
fect, each (explicit) path is associated not just with a 
single value specification, but with a whole family of 
specifications indexed by extensions of those paths. 
This suggests the following approach to the se- 
mantics of defaults in DATR. Rather than interpre- 
ting node definitions (in a given global context) as 
partial functions from paths to values (i.e. of type 
U* --+ U*) we choose instead to interpret them as 
partial functions from (explicit) paths, to functions 
from extensions of those paths to values (i.e. of type 
U* -+ (U* --+ U*)). Now suppose that f : U* --~ 
(U* --~ U*) is the function associated with the node 
definition T/N in a given DATR interpretation. We 
can define a partial function A(f) : U* --~ U* (the 
default interpretation of T/N) as follows. For each 
v E U* set 
A(f)(v) = f(vl)(V2) 
where v = vlv2 and vx is the longest prefix of v 
such that f(vl) is defined. In effect, the function 
A(f) makes explicit that information about paths 
and values that is only implicit in f, but just in so 
far as it does not conflict with explicit information 
provided by f. 
In order to re-interpret node definitions in the 
manner suggested above, it is necessary to modify 
the interpretation of value descriptors. In a given 
global context c, a value descriptor d now corre- 
sponds to a total function \[d\]~ : U* --+ U* (intui- 
tively, a function from path extensions to values). 
For example, atoms now denote constant functions: 
\[a\]c(v) = F(a) for all v G U" 
More generally, value descriptors will denote dif- 
ferent values for different paths. Figure 4 shows the 
revised clause for global node/path pairs, the other 
definitions being very similar. Note the way in which 
the 'path' argument v is used to extend Vl ...vn in 
order to define the new local (and in this case also, 
global) context c ~. On the other hand, the meaning 
of each of the di is obtained with respect to the 'em- 
pty path' e (i.e. path extension does not apply to 
subterms of inheritance descriptors). 
As before, the interpretation function is extended 
to sequences of path descriptors, so that for ¢ = 
dl...d, (n >_ o) we have \[¢\]~(v) = Vl...v, G V*, if 
vi = Idil(v) is defined, for each i (1 < i < n) (and 
\[¢\],(v) is undefined otherwise). The definition of 
the interpretation of node definitions can be taken 
over unchanged from the previous section. However, 
for a theory T and node N, the function \[T/N\]e is 
now of type U* --+ (U* ~ U*). An interpretation 
I = (U, x, F) is a default model for theory T just in 
case for every context c and node N we have: 
IN\], _~ A(IT"/NI,) 
As an example, consider the default interpretation 
of the definition of the node Walk given above. By 
60 
\["N: (dl'-"dn)"\]c(v) ={ 
if v, = \[dil¢(e) is defined for each i(1 < i < n), then 
~(d)(d) where c'= (f(g),vl...vnv) 
undefined otherwise 
Figure 4: Revised denotation for global node/path pairs 
definition, any default model of the theory of figure 1 
must respect the following containment: 
\[W kL 
((mor root), Av.walk)} 
/,From the definition of A, it follows that for any 
path v, if v extends (mor root), then it is mapped 
onto the value walk, and otherwise it is mapped to 
the value given by \[Verb : 0It(v). We have the 
following picture: 
\[Walklc _D {(0, \[Verb: Oft(O)), 
((mor), \[Verb: Olc((mor))), 
((mor root), walk), 
((mor root root), walk), 
• . .} 
The default models of a theory 7" constitute a pro- 
per subset of the models ofT: just those that respect 
the default interpretations of each of the nodes defi- 
ned within the theory. 
5 Conclusions 
The work described in this paper fulfils one of the 
objectives of the DATR programme: to provide the 
language with an explicit, declarative semantics. We 
have presented a formal model of DATR as a lan- 
guage for defining partial functions and this model 
has been contrasted with an informal view of DATR 
as a language for representing inheritance hierar- 
chies. The approach provides a transparent treat- 
ment of DATR's notion of (local and global) context 
and accounts for DATR's default mechanism by re- 
garding value descriptors (semantically) as families 
of values indexed by paths. 
The provision of a formal semantics for DATR 
is important for several reasons. First, it provi- 
des the DATR user with a concise, implementation- 
independent account of the meaning of DATR theo- 
ries. Second, it serves as a standard against which 
other, operational definitions of the formalism can 
be judged. Indeed, in the absence of such a stan- 
dard, it is impossible to demonstrate formally the 
correctness of novel implementation strategies (for 
an example of such a strategy, see (Langer, 1994)). 
Third, the process of formalisation itself aids our 
understanding of the language and its relationship 
to other non-monotonic, attribute-value formalisms. 
Finally, the semantics presented in this paper provi- 
des a sound basis for subsequent investigations into 
the mathematical and computational properties of 
DATR. 
6 Acknowledgements 
The author would like to thank Roger Evans, Gerald 
Gazdar, Bill Rounds and David Weir for helpful dis- 
cussions on the work described in this paper. 

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